Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.cdtb)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=43/8, b>=a

For fixed z and a=43/8, b=45/8

http://functions.wolfram.com/07.23.03.cdtb.01

Input Form

Hypergeometric2F1[43/8, 45/8, -(11/2), z] == (1/(11669504 (1 - z)^(33/2))) (Sqrt[1 - z] (11669504 - 254143232 z + 2797374048 z^2 - 21409030983 z^3 + 136328883096 z^4 - 891426468324 z^5 + 10843233810472 z^6 + 68713990688246 z^7 + 83498274369192 z^8 + 29962252766428 z^9 + 2935150313144 z^10 + 43419498969 z^11) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (8752128 - 191883776 z + 2125029732 z^2 - 16345932039 z^3 + 104409006184 z^4 - 682144589028 z^5 + 24586291785504 z^6 + 99157810840630 z^7 + 101210039034936 z^8 + 32863277218908 z^9 + 3027794211932 z^10 + 43419498969 z^11) Sin[(3 ArcSin[Sqrt[z]])/4])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]